Abstract: In this article we obtain the Horn-Li-Merino formula for computing the gap as well as the spherical gap between two densely defined unbounded closed operators. As a consequence we prove that the gap and the spherical gap of an unbounded closed operator are and respectively. With the help of these formulae we establish a relation between the spherical gap and the gap of unbounded closed operators. We discuss some properties of the spherical gap similar to those of the gap metric.

1.N.
I. Akhiezer and I.
M. Glazman, Theory of linear operators in Hilbert space, Dover
Publications, Inc., New York, 1993. Translated from the Russian and with a
preface by Merlynd Nestell; Reprint of the 1961 and 1963 translations; Two
volumes bound as one. MR
1255973

N. I. Akhiezer and I. M. Glazman, Theory of linear operators in Hilbert space, Dover Publications. Inc., New York, 1993. Translated from the Russian and with a preface by Merlynd Nestell. Reprint of the 1961 and 1963 translations, two volumes bound as one. MR 1255973 (94i:47001)